An Efficient Distributed Parallel Algorithm for Optimal Consensus of Multi-Agent Systems

A parallel algorithm is presented in this paper to efficiently solve the optimal consensus problem of multi-agent systems. By utilizing a Jacobi -type proximal alternating direction multiplier framework, the optimization process is divided into two independent subproblems that can be solved in parallel to improve computational efficiency, followed by the Lagrangian multiplier update. The convergence analysis of the proposed algorithm is performed using the convex optimization theory, deriving the convergence conditions concerning the auxiliary parameters. Furthermore, the accelerated algorithm enjoys a convergence rate of $\mathcal {O}(\frac{1}{t^{2}})$ by adjusting the auxiliary parameters adaptively. To leverage the strengths of the collaboration of multi-agent systems, the distributed implementation of the proposed parallel algorithm is further developed, where each agent addresses its private subproblems only using its own and its neighbor's information. Numerical simulations demonstrate the effectiveness of the theoretical results.